diff --git a/tests/python/zlktree.ipynb b/tests/python/zlktree.ipynb
index c3b636caa..b7675ccdf 100644
--- a/tests/python/zlktree.ipynb
+++ b/tests/python/zlktree.ipynb
@@ -216,7 +216,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5115790270> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced67112a0> >"
       ]
      },
      "execution_count": 2,
@@ -640,7 +640,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4ec00> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599cfc0> >"
       ]
      },
      "execution_count": 10,
@@ -1063,7 +1063,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4ea20> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599c600> >"
       ]
      },
      "execution_count": 11,
@@ -1256,7 +1256,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4ef60> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599c0c0> >"
       ]
      },
      "execution_count": 13,
@@ -1701,7 +1701,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4e8d0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599c450> >"
       ]
      },
      "execution_count": 14,
@@ -2096,7 +2096,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a614b0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad600> >"
       ]
      },
      "metadata": {},
@@ -2427,7 +2427,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a61510> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad5d0> >"
       ]
      },
      "metadata": {},
@@ -2513,7 +2513,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a61030> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad1e0> >"
       ]
      },
      "metadata": {},
@@ -2624,7 +2624,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a61480> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad270> >"
       ]
      },
      "metadata": {},
@@ -2662,7 +2662,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a611b0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad150> >"
       ]
      },
      "metadata": {},
@@ -2700,7 +2700,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a610c0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59ad1b0> >"
       ]
      },
      "metadata": {},
@@ -3862,7 +3862,7 @@
        "};$(\"#acdaut0 #E9\").addClass(\"acdN0\");$(\"#acdaut0 #E10\").addClass(\"acdN0\");$(\"#acdaut0 #E11\").addClass(\"acdN0\");$(\"#acdaut0 #E12\").addClass(\"acdN0\");$(\"#acdaut0 #E13\").addClass(\"acdN0\");$(\"#acdaut0 #E14\").addClass(\"acdN0\");$(\"#acdaut0 #E15\").addClass(\"acdN0\");$(\"#acdaut0 #E16\").addClass(\"acdN0\");$(\"#acdaut0 #E21\").addClass(\"acdN0\");$(\"#acdaut0 #E22\").addClass(\"acdN0\");$(\"#acdaut0 #E23\").addClass(\"acdN0\");$(\"#acdaut0 #E24\").addClass(\"acdN0\");$(\"#acdaut0 #E25\").addClass(\"acdN0\");$(\"#acdaut0 #E26\").addClass(\"acdN0\");$(\"#acdaut0 #E27\").addClass(\"acdN0\");$(\"#acdaut0 #E28\").addClass(\"acdN0\");$(\"#acdaut0 #E33\").addClass(\"acdN0\");$(\"#acdaut0 #E34\").addClass(\"acdN0\");$(\"#acdaut0 #E35\").addClass(\"acdN0\");$(\"#acdaut0 #E36\").addClass(\"acdN0\");$(\"#acdaut0 #E31\").addClass(\"acdN1\");$(\"#acdaut0 #E32\").addClass(\"acdN1\");$(\"#acdaut0 #E39\").addClass(\"acdN1\");$(\"#acdaut0 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#E33\").click(function(){acd0_edge(33);});$(\"#acdaut0 #E34\").click(function(){acd0_edge(34);});$(\"#acdaut0 #E35\").click(function(){acd0_edge(35);});$(\"#acdaut0 #E36\").click(function(){acd0_edge(36);});$(\"#acdaut0 #E37\").click(function(){acd0_edge(37);});$(\"#acdaut0 #E38\").click(function(){acd0_edge(38);});$(\"#acdaut0 #E39\").click(function(){acd0_edge(39);});$(\"#acdaut0 #E40\").click(function(){acd0_edge(40);});$(\"#acdaut0 #S0\").click(function(){acd0_state(0);});$(\"#acdaut0 #S1\").click(function(){acd0_state(1);});$(\"#acdaut0 #S2\").click(function(){acd0_state(2);});$(\"#acdaut0 #S3\").click(function(){acd0_state(3);});$(\"#acdaut0 #S4\").click(function(){acd0_state(4);});$(\"#acdaut0 #S5\").click(function(){acd0_state(5);});$(\"#acdaut0 #S6\").click(function(){acd0_state(6);});$(\"#acdaut0 #S7\").click(function(){acd0_state(7);});$(\"#acdaut0 #S8\").click(function(){acd0_state(8);});$(\"#acdaut0 #S9\").click(function(){acd0_state(9);});$(\"#acd0 #N0\").click(function(){acd0_node(0, 0);});$(\"#acd0 #N1\").click(function(){acd0_node(1, 1);});$(\"#acd0 #N2\").click(function(){acd0_node(2, 1);});$(\"#acd0 #N3\").click(function(){acd0_node(3, 1);});$(\"#acd0 #N4\").click(function(){acd0_node(4, 1);});$(\"#acd0 #N5\").click(function(){acd0_node(5, 1);});$(\"#acd0 #N6\").click(function(){acd0_node(6, 1);});$(\"#acd0 #N7\").click(function(){acd0_node(7, 1);});$(\"#acd0 #N8\").click(function(){acd0_node(8, 1);});$(\"#acd0 #N9\").click(function(){acd0_node(9, 0);});$(\"#acd0 #N10\").click(function(){acd0_node(10, 0);});$(\"#acd0 #N11\").click(function(){acd0_node(11, 0);});$(\"#acd0 #N12\").click(function(){acd0_node(12, 0);});$(\"#acd0 #N13\").click(function(){acd0_node(13, 0);});$(\"#acd0 #N14\").click(function(){acd0_node(14, 0);});</script>"
       ],
       "text/plain": [
-       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7f5114a59630> >"
+       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7fced59ade40> >"
       ]
      },
      "execution_count": 18,
@@ -4042,7 +4042,7 @@
     }
    ],
    "source": [
-    "theacd.step(7, 11)"
+    "theacd.step(8, 11)"
    ]
   },
   {
@@ -4054,7 +4054,7 @@
     {
      "data": {
       "text/plain": [
-       "(8, 0)"
+       "(4, 1)"
       ]
      },
      "execution_count": 25,
@@ -4063,7 +4063,7 @@
     }
    ],
    "source": [
-    "theacd.step(13, 13)"
+    "theacd.step(4, 13)"
    ]
   },
   {
@@ -4079,7 +4079,9 @@
     "\n",
     "Let's consider the first step.  Node 4 does not contains edge 11, so we move up the tree until we find node 0 that contains it, and emit level 0.  Then the destination of edge 11 is 3, so we consider the subtree associated to 3 (clicking on state 3 shows us this is the tree that has nodes 4,7,13 as leaves) and return the left-most node of the next branch: 12.\n",
     "\n",
-    "When we read edge 13 from node 12, go all the way up to node 0 again, and consider the left-most node of the next branch in the tree for the destination 2: that's node 7."
+    "When we read edge 13 from node 12, go all the way up to node 0 again, and consider the left-most node of the next branch in the tree for the destination 2: that's node 8.  \n",
+    "\n",
+    "Reading edges 11 and 13 will get us back to node 4. If we repeat this infinitely often, the smallest level we will see infinitely often is therefore 0, meaning that is a rejecting cycle."
    ]
   },
   {
@@ -4735,7 +4737,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a6a480> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599c210> >"
       ]
      },
      "execution_count": 27,
@@ -4754,7 +4756,7 @@
    "id": "f039aeaa",
    "metadata": {},
    "source": [
-    "Note how the loops `2#4 → 3#4 → 2#4` and `2#4 → 3#12 → 2#7 → 3#13 → 2#4` corresponds to the two cycles stepped though before."
+    "Note how the cycles `2#4 → 3#4 → 2#4` and `2#4 → 3#12 → 2#8 → 3#4 → 2#4` corresponds to the two cycles stepped though before."
    ]
   },
   {
@@ -5374,7 +5376,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a611b0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced599c720> >"
       ]
      },
      "execution_count": 29,
@@ -5603,7 +5605,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4e4e0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59b53c0> >"
       ]
      },
      "execution_count": 33,
@@ -5715,7 +5717,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7f5114a4e090> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fced59b5e70> >"
       ]
      },
      "execution_count": 34,
@@ -5881,7 +5883,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a4eed0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59b5660> >"
       ]
      },
      "execution_count": 35,
@@ -6174,7 +6176,7 @@
        "};$(\"#acdaut1 #E1\").addClass(\"acdN0\");$(\"#acdaut1 #E2\").addClass(\"acdN0\");$(\"#acdaut1 #E3\").addClass(\"acdN0\");$(\"#acdaut1 #E4\").addClass(\"acdN0\");$(\"#acdaut1 #E5\").addClass(\"acdN0\");$(\"#acdaut1 #E6\").addClass(\"acdN0\");$(\"#acdaut1 #E7\").addClass(\"acdN0\");$(\"#acdaut1 #E8\").addClass(\"acdN0\");$(\"#acdaut1 #E6\").addClass(\"acdN1\");$(\"#acdaut1 #E1\").click(function(){acd1_edge(1);});$(\"#acdaut1 #E2\").click(function(){acd1_edge(2);});$(\"#acdaut1 #E3\").click(function(){acd1_edge(3);});$(\"#acdaut1 #E4\").click(function(){acd1_edge(4);});$(\"#acdaut1 #E5\").click(function(){acd1_edge(5);});$(\"#acdaut1 #E6\").click(function(){acd1_edge(6);});$(\"#acdaut1 #E7\").click(function(){acd1_edge(7);});$(\"#acdaut1 #E8\").click(function(){acd1_edge(8);});$(\"#acdaut1 #S0\").click(function(){acd1_state(0);});$(\"#acdaut1 #S1\").click(function(){acd1_state(1);});$(\"#acd1 #N0\").click(function(){acd1_node(0, 1);});$(\"#acd1 #N1\").click(function(){acd1_node(1, 0);});</script>"
       ],
       "text/plain": [
-       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7f5114a6e570> >"
+       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7fced59bb180> >"
       ]
      },
      "execution_count": 37,
@@ -6297,7 +6299,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a6e2a0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59bb060> >"
       ]
      },
      "execution_count": 38,
@@ -6635,7 +6637,7 @@
        "};$(\"#acdaut2 #E1\").addClass(\"acdN0\");$(\"#acdaut2 #E2\").addClass(\"acdN0\");$(\"#acdaut2 #E3\").addClass(\"acdN0\");$(\"#acdaut2 #E4\").addClass(\"acdN0\");$(\"#acdaut2 #E5\").addClass(\"acdN0\");$(\"#acdaut2 #E6\").addClass(\"acdN0\");$(\"#acdaut2 #E7\").addClass(\"acdN0\");$(\"#acdaut2 #E1\").addClass(\"acdN1\");$(\"#acdaut2 #E3\").addClass(\"acdN1\");$(\"#acdaut2 #E4\").addClass(\"acdN1\");$(\"#acdaut2 #E5\").addClass(\"acdN1\");$(\"#acdaut2 #E7\").addClass(\"acdN2\");$(\"#acdaut2 #E1\").click(function(){acd2_edge(1);});$(\"#acdaut2 #E2\").click(function(){acd2_edge(2);});$(\"#acdaut2 #E3\").click(function(){acd2_edge(3);});$(\"#acdaut2 #E4\").click(function(){acd2_edge(4);});$(\"#acdaut2 #E5\").click(function(){acd2_edge(5);});$(\"#acdaut2 #E6\").click(function(){acd2_edge(6);});$(\"#acdaut2 #E7\").click(function(){acd2_edge(7);});$(\"#acdaut2 #S0\").click(function(){acd2_state(0);});$(\"#acdaut2 #S1\").click(function(){acd2_state(1);});$(\"#acdaut2 #S2\").click(function(){acd2_state(2);});$(\"#acdaut2 #S3\").click(function(){acd2_state(3);});$(\"#acd2 #N0\").click(function(){acd2_node(0, 1);});$(\"#acd2 #N1\").click(function(){acd2_node(1, 0);});$(\"#acd2 #N2\").click(function(){acd2_node(2, 0);});</script>"
       ],
       "text/plain": [
-       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7f5114a6e2d0> >"
+       "<spot.acd; proxy of <Swig Object of type 'spot::acd *' at 0x7fced59bb480> >"
       ]
      },
      "execution_count": 40,
@@ -6763,7 +6765,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a6e930> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59bba50> >"
       ]
      },
      "execution_count": 41,
@@ -7043,7 +7045,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a6e630> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59bb360> >"
       ]
      },
      "execution_count": 42,
@@ -7137,7 +7139,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5114a6ef00> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced59bbf30> >"
       ]
      },
      "execution_count": 43,
@@ -7248,7 +7250,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f51027c83c0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fced474f300> >"
       ]
      },
      "execution_count": 45,